CHRISTIANE AMANPOUR, CNN ANCHOR: Tonight, President Obama makes his first foray into the Middle East peace swap, but is he already making a U­turn?

Good evening. I’m Christiane Amanpour, and welcome again to our new program, where we take the big story and try to bring it more depth and understanding.

So at the U.N. today, President Obama called for peace talks to resume, but has his opening gambit already failed? After meeting with the Israeli prime minister, Benjamin Netanyahu, and the Palestinianpresident, Mahmoud Abbas, here in New York, he dropped the U.S. demand for an Israeli settlement freeze before starting talks. And when it comes to a peace deal, what do the Palestinians think?

We go now straight to an exclusive new poll that may offer some hope. Joining me now from the U.N., straight from a luncheon with President Obama and world leaders, is Terje Roed­Larsen, the president of the International Peace Institute that commissioned this poll, and also a U.N. special representative.

AMANPOUR: I just want to go straight to some of the key findings in this poll. We’ve got some full screens of this to show, and it’s about the popularity. President Mahmoud Abbas’ popularity seems to be rising — 55 percent of the Palestinians say they are satisfied — whereas Prime Minister Ismail Haniyeh of Hamas, his popularity seems to be decreasing — 32 percent, apparently, say they’re satisfied with him, while 64 percent say they’re dissatisfied.

Now, on the issue of a Palestinian state, according to your poll, 55 percent of Palestinians say that they want the two­state solution in the West Bank and Gaza separate from Israel, whereas only 11 percent are saying that there is a one­state solution to all of this.

So, Mr. Larsen, what is the good news here?

ROED­LARSEN: I think this brand­new IPI poll brings very good news to the Palestinians and to all those who are working for peace in the Middle East, because there is here now major shifts. The Palestinians, now a vast majority, wants their leaders to go back to the table. A vast majority wants to have a two­state solution. And even more, the Palestinians now, compared with 2000 during the Camp David negotiations, they’re much more open­minded about making painful compromises in order to establish a Palestinian state.

So this is all good news for everybody, except Hamas, who’s now — where the pendulum has swung since they formed a government in 2006. Now Mahmoud Abbas, Abu Mazen, has a vast majority — vast majority support compared with Haniyeh, and Fatah would win a landslide victory in parliamentary elections.

AMANPOUR: So that’s the key there, in terms of who would win the parliamentary elections? ROED­LARSEN: Yes, this is very good news for all those who are working for peace in the Middle East, but

it’s particularly good news for the Palestinian Authority and for Fatah.

AMANPOUR: Mr. Larsen, thank you so much, indeed, for joining us from the U.N. And we will back with you for more on this in the days and weeks to come.

But right now, we’re joined here in the studio by Saeb Erakat, the chief negotiator for the Palestinians on the peace process, and live from Jerusalem, Dan Meridor, the Israeli deputy prime minister and minister of intelligence.

Thank you both very much for joining me on this.

Can I first ask you, Mr. Meridor, you heard that poll. You heard Mr. Larsen. Israel is always saying it does not have a partner for peace. Are you now convinced that there is, in fact, one?

DAN MERIDOR, ISRAELI DEPUTY PRIME MINISTER: I very much hope so. Of course, Mr. Abu Mazen is not at all in control of Gaza. Gaza was taken away by Hamas (inaudible) so how to deal with Hamas and make Abu Mazen the sole representative is their concern and our concern. We want to have a negotiator. I hope it is Mr. Abu Mazen. If the polls are right, his popularity grows, it’s good news.

AMANPOUR: What does that mean then, Mr. Erakat, that there is this rise in popularity for your president, Abu Mazen, Mahmoud Abbas, and a decrease for Ismail Haniyeh, and potentially Fatah, if they run a good campaign, the poll says could win? Does it make a difference whether they get Gaza or not? Or could they even win in Gaza?

I think this is significant poll. I really think that President Abbas has been exerting every possible effort, number one, to get the one authority, one gun, the rule of law. He ended the chaos and lawlessness in the West Bank. He has a government of transparency, accountability. So people are responding to that, which shows clearly that Palestinians want nothing more in their lives than to achieve peace on the basis of a two­ state solution.